Varieties of positive modal algebras and structural completeness
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F19%3A00504824" target="_blank" >RIV/67985807:_____/19:00504824 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/S1755020319000236" target="_blank" >http://dx.doi.org/10.1017/S1755020319000236</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S1755020319000236" target="_blank" >10.1017/S1755020319000236</a>
Alternative languages
Result language
angličtina
Original language name
Varieties of positive modal algebras and structural completeness
Original language description
Positive modal algebras are the〈∧,∨, 3, D, 0, 1〉-subreducts of modal algebras. We show that the variety of positive interior algebras is not locally finite. However, the free one-generated positive interior algebra has 37 elements. Moreover, we show that there are exactly 16 varieties of height at most 4 in the lattice of varieties of positive interior algebras. Building on this, we infer that there are only 3 non-trivial structurally complete varieties of positive K4-algebras. These are also the unique non-trivial hereditarily structurally complete such varieties. Moreover, we characterize passively structurally complete varieties of positive K4-algebras and show that there are infinitely many of them. These results are related to the study of structurally complete axiomatic extensions of an algebraizable Gentzen system for positive modal logic.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Review of Symbolic Logic
ISSN
1755-0203
e-ISSN
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Volume of the periodical
12
Issue of the periodical within the volume
3
Country of publishing house
GB - UNITED KINGDOM
Number of pages
32
Pages from-to
557-588
UT code for WoS article
000483091300006
EID of the result in the Scopus database
2-s2.0-85067359071